High School Cluster Quiz Radical



Radical FunctionsGiven the function y=-x+9-2,Plot a point on the coordinate grid to show the x-intercept of the function.Plot a point on the coordinate grid to show the y-intercept of the function.Given the function y=38-x+1,Plot a point on the coordinate grid to show the x-intercept of the function.Plot a point on the coordinate grid to show the y-intercept of the function.Enter the value of x that makes the equation true.x-4=7Enter the values of y that make the equation true. -y5= 33-ySelect whether each equation has no real solutions, one real solution, or infinitely many real solutions.EquationNo Real SolutionsOne Real SolutionInfinitely Many Real Solutions3-x=x-4-2x+3=03x+x=x(3x+1)A student was finding the solution to the equation 3+4-x=2 and wrote the five steps shown.Step 1: 4-x=-1Step 2: (4-x)2=(-1)2Step 3: 4-x=1Step 4: 4-1=xStep 5: 3 = xThe student states that x = 3 is the solution to the equation 3+4-x=2.Explain why x = 3 cannot be a solution to the equation 3+4-x=2. Use evidence from the equation 3+4-x=2 in your explanation.Blake was finding the solutions to the equation x3+17=4+x2 and wrote the steps shown.Step 1: x3+17=8+x2Step 2: (x3+17)2=(8+x2)2Step 3: x3+17=64+16x+x24Step 4: 4x3+68=64+16x+x2Step 5: 4x3-x2-16x+4=0Step 6: x-2x+24x-1=0Step 7: x = 2, –2, and 0.25Blake thinks that –2 cannot be a solution to the original equation because (–2)3 would be a negative value and you cannot have a negative value under a square root in the original equation. Blake points to step 2 as the step that produced the erroneous answer of –2.Do you agree to disagree with Blake? Explain why.Determine whether each statement is True for All values of x, True for Some values of x, or Not True for Any values of x.StatementTrue for AllTrue for SomeNot True for AnyIf x=y, then x2=y2If x2=y2, then x=yIf x2=y, then x=yTeacher MaterialA-SSE.AInterpret the structure of expressions.A-CED.ACreate equations that describe numbers or relationships.A-REI.AUnderstand solving equations as a process of reasoning and explain the reasoning.F-IF.AUnderstand the concept of a function and use function notation.F-IF.CAnalyze functions using different representations.F-BF.ABuild a function that models a relationship between two quantities.QuestionClaimKey/Suggested Rubric112 points: Plots a point at (0, 1) AND a point at (5, 0).1 point: Plots a point at (0, 1) OR a point at (5, 0).2112 points: Plots a point at (0, 3) AND a point at (9, 0).1 point: Plots a point at (0, 3) OR a point at (9, 0).311 point: x = 53411 point: Writes 3 values for y: one in the interval –12.5 to –12.4, inclusive, one in the interval 3.2 to 3.3, inclusive, and one in the interval 9.1 to 9.2, inclusive.5211 point:EquationNo Real SolutionsOne Real SolutionInfinitely Many Real Solutions3-x=x-4x-2x+3=x3x+x=x(3x+1)x631 point: Answers will vary. Example: x can’t be 3 because there is no real solution to the equation. The equation says that 3 plus some number is 2, which means that number has to be equal to –1. But the square root of a real number can’t be –1, so x can’t be equal to 3.7431 point: The student disagrees with Blake and shows or explains how –2 (or any negative number less than the cubed root of 17) can be a solution to the original equation.NOTE: No credit is earned for simply disagreeing with Blake.8431 point:StatementTrue for AllTrue for SomeNot True for AnyIf x=y, then x2=y2xIf x2=y2, then x=yxIf x2=y, then x=yx ................
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